巨磁涡旋弦的严格分析
Rigorous analysis of giant magnetic vortex strings
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中文总结 AI 辅助
本文对四次阿贝尔-希格斯模型中大磁通量涡旋的磁芯半径进行了严格渐近分析，证明了其与物理预测一致，并揭示了与Ginzburg-Landau理论的深层联系。
中文摘要 AI 辅助
本文研究四次阿贝尔-希格斯模型中轴向对称的Abrikosov-Nielsen-Olesen涡旋，当磁通量变得任意大时的情况。重点在于发展Hakim、Lemaitre和Mallick '01以及Dumitrescu、Gaikwad '25的正式大通量展开背后的严格渐近分析。对于每个小于4的耦合常数，我们证明了磁芯半径的大小与物理学文献所预测的一致。我们将正常态与超导态之间的界面与Ginzburg-Landau理论中的经典正常-超导转变层进行识别。Chapman-Howison-McLeod-Ockendon '91的定理证明了其存在性、唯一性和单调性。左侧标量场的高斯尾部与界面的联系直接通过Weber方程建立。在左侧重叠区域，核心希格斯方程被视为半经典Sturm-Liouville问题，其中希格斯场像高斯函数一样衰减。外部区域则围绕修正贝塞尔函数进行微扰描述。一个关键步骤是证明线性化界面方程两端允许的柯西数据之间的匹配映射具有最大秩。
英文摘要
This paper studies axially symmetric Abrikosov-Nielsen-Olesen vortices in the quartic Abelian Higgs model as the magnetic flux becomes arbitrarily large. The emphasis is on developing the rigorous asymptotic analysis behind the formal large-flux expansions of Hakim, Lemaitre, and Mallick '01 and Dumitrescu, Gaikwad '25. For every coupling constant less than 4 we prove that the radius of the magnetic core is of the size predicted by the physics literature. We identify the interface between then normal and super-conducting regimes with the classical normal-to-superconducting transition layer in Ginzburg-Landau theory. The theorem of Chapman-Howison-McLeod-Ockendon '91 proves its existence, uniqueness and monotonicity. The connection of the Gaussian tail of the scalar field on the left with the interface is made directly with the Weber equation. The core Higgs equation is treated as a semiclassical Sturm-Liouville problem in the left overlap region, where the Higgs field decays like a Gaussian. The exterior region is described perturbatively around modified Bessel functions. A key step is to show that the matching map between the admissible Cauchy data at the two ends of the linearized interface equations has maximal rank.
发表机构
- California Institute of Technology（加州理工学院）
- Yale University（耶鲁大学）
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